Equivalence theorem for light waves on scattering from particle collections with anisotropic random distributions

We report the equivalence theorem for light waves on scattering from particle collections with anisotropic distributions. Our findings indicate that different particle collections with anisotropic distributions can generate scattered fields exhibiting identical spectral density or spectral degree of coherence across different dimensions, provided that certain conditions are satisfied. As an example, we investigate the scattering of light waves from collections of Gaussian-correlated, determinate particles with quasi-homogeneous, anisotropic distributions, and we derive the conditions for achieving identical normalized spectral density and spectral degree of coherence across the entire space, specific planes, and specific lines. Additionally, we discuss the implications of the equivalence theorem for the inverse scattering problem. Our work is anticipated to extend the weak scattering equivalence theorem and may assist in guiding accurate measurements of anisotropic medium information in the inverse scattering problem.